Tumblr decided to revoke my API keys yesterday. I am in contact with them and am trying to negotiate to get them restored. Fingers crossed…
The Tumblr stack still functions. However, it will only pulls down a limited number of posts for now. Links to individual blog posts will still function as well so you are fine in terms of SEO.
Good news. Tumblr reinstated my API key. However, they have only done so for 30 days. I have requested that they extend this until at least the end of January. I have not heard back yet.
This at least gets your sites back up and running. Now I have 30 days to figure out a solution.
Great news! Thanks for the support Joe. 
We have 28 website clients using the tumblr stack who are now happy again. I’m confident that you will find a good solution.
It’s December 7th and the Tumblr stack is still working. Good thing because we still have lots of websites to update. Did they extend the date for you?
Nope, Joe was just as surprised as you were. Just have to wait and see what happens…
Yes. I never heard back from Tumblr but everything does indeed still work. #knockonwood
In case you missed this thread… TotalMove (beta) - Migrate from Tumblr to Total CMS